Holographic equilibration under external dynamical electric field

The holographic equilibration of a far-from-equilibrium strongly coupled gauge theory is investigated. In particular, the dynamics of a probe D7-brane in an AdS-Vaidya background is studied in the presence of an external time-dependent electric field. Defining the equilibration times teqc and teqj, at which condensation and current relax to their final equilibrated values, receptively, the smallness of transition time kM or kE is enough to observe a universal behaviour for re-scaled equilibration times kMkE(teqc)−2 and kMkE(teqj)−2. kM(kE) is the time interval in which the temperature (electric field) increases from zero to finite value. Moreover, regardless of the values for kM and kE, teqc/teqj also behaves universally for large enough value of the ratio of the final electric field to final temperature. Then a simple discussion of the static case reveals that teqc≤teqj. For an out-of-equilibrium process, our numerical results show that, apart from the cases for which kE is small, the static time-ordering, that is teqc≤teqj, persists.